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Home » So \(a_5 = 13\) - IX Labs

So \(a_5 = 13\) - IX Labs

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Question: Find the largest value of $ x $ that satisfies $ |2x - 5| + |x + 3| = 12 $.

📌 Solution: We analyze the expression by considering the critical points where expressions inside absolute values change sign: $ x = \frac{5}{2} $ and $ x = -3 $. We consider three intervals:

📌 $ x < -3 $:

📌 Then $ 2x - 5 < 0 $, $ x + 3 < 0 $, so:

📌 -(2x - 5) - (x + 3) = -2x + 5 - x - 3 = -3x + 2 = 12 \Rightarrow -3x = 10 \Rightarrow x = -\frac{10}{3} \approx -3.33

📌 But $ -\frac{10}{3} < -3 $, so valid.

📌 $ -3 \le x < \frac{5}{2} $:

📌 Then $ 2x - 5 < 0 $, $ x + 3 \ge 0 $, so:

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